What is inverse property in math?

Answers

Answer 1

Answer:

The inverse property definition states when added together with its additive inverse, the sum of the two numbers will be zero. When a number is multiplied by its multiplicative inverse, the product will be one

Step-by-step explanation:


Related Questions

Graph the line with slope of 3/4 passing through the point (-1, 2)

Answers

Answer:

Step-by-step explanation:

Use the graph of the function to find the domain and range of f (Enter your answers using interval notation)

Answers

In the given graph the domain and range of function y=f(x) is

Domain: (-2,2]

Range : [-4, 5)

What is domain and range?

A function's domain is the set of all possible inputs to the function. This means it can be any number that can be entered into a function. For the majority of functions, this will be any number that can be substituted for the letter x. Except for a few exceptions such as square root functions and rational numbers, your domain will almost always be all real numbers.

The set of all possible outputs of a function is referred to as its range. This is usually represented by the letters y or f(x). The range is any number obtained by substituting any number for x.

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A guy wire attached to the top of a radio antenna

is bolted to the ground 48 m from the base of

the tower. If the wire makes an angle of 14°

with the ground. What is the length of the

guy wire? Round your answer to the nearest

hundredth of a meter.

1

Answers

The length of the guy wire is 48.87 m.

How to find the length?

To find the length of the guy wire, you can use the formula for the length of a side of a right triangle (the Pythagorean theorem): [tex]c = sqrt(a^2 + b^2)[/tex]. In this case, c is the length of the guy wire, a is the distance from the base of the tower to the point where the guy wire is attached to the ground (48 m), and b is the distance from the point where the guy wire is attached to the ground to the top of the antenna.

To find b, you can use the tangent function: [tex]tan(14°) = b / 48.[/tex]

Solving for b gives b = 6.78 m

Then, length of wire can be calculated as

[tex]c = sqrt(48^2 + 6.78^2)[/tex]

[tex]c = 48.87 m (approx)[/tex]

Rounding it to the nearest hundredth of a meter, the length of the guy wire is 48.87 m.

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Which of the following are irrational numbers?
Choose two correct answers.
3.05
√17
√27
√81

Answers

Answer:√17

              √81

                √27

This 3 numbers are irrational number

Answer:

17 and 27 are irrational

Step-by-step explanation:

Math Subject: Symmetry.

Question is attached below.

Answers

The term "line of symmetry" refers to the fictitious axis or line that you fold a figure along to create its symmetrical halves.

What is Symmetry?

A definition of symmetry states that whether one form is moved, rotated, or flipped, it looks precisely like the other shape. Just fold the paper, draw one-half of the heart at the fold, then cut it out to discover that the second half precisely matches the first half when you are instructed to cut out a "heart" from a sheet of paper. The heart-shaped carving is an illustration of symmetry.

Symmetry is defined in mathematics as "a mirror image." Symmetry is the property of an image that remains unchanged after a form has been rotated or flipped. There are patterns in it. In daily life, you may have heard the word "symmetrical" frequently. One half of a thing is the mirror image of the other half, which is a balanced and proportionate likeness. Asymmetrical refers to a form that is not symmetrical. In nature, architecture, and the arts, symmetrical things are all around us.

The term "line of symmetry" refers to the fictitious axis or line that you fold a figure along to create its symmetrical halves. In essence, it splits one thing into two mirror images. The symmetry line may run vertically, horizontally, or diagonally. There might be one or many symmetry lines.

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Answer:

1. Choose Your Shape: Start with a shape that you want to create a line of symmetry for. It could be a simple shape like a square, rectangle, or triangle.

2. Draw the Shape: Draw the shape neatly on a piece of paper using a pencil.

3. Identify the Line of Symmetry: Decide where you want to place the line of symmetry. This line should divide the shape into two equal halves.

4. Draw the Line of Symmetry: Draw a straight line through the center of the shape, from one side to the other. Use a ruler to ensure the line is straight and passes through the center.

5. Create the Mirror Image: To create the mirror image on the other side of the line, imagine that the line is a mirror. Reflect each point on one side of the line to the other side while maintaining the same distance from the line. You can also use a ruler or straightedge to guide you as you draw.

6. Check for Symmetry: Carefully examine both sides of the line to make sure they are mirror images of each other. The distances and angles should match.

7. Finalize the Drawing: Once you're satisfied with the symmetry, trace over your pencil lines with a pen or darken them to make your drawing more prominent.

8. Erase Construction Lines: Gently erase any construction lines or guidelines you drew in the earlier steps.

Salma's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Salma $5.60 per pound, and type B coffee costs $4.40 per pound. This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $451.20. How many pounds of type A coffee were used?

Answers

Answer: hi

11,28 pound / usd

Step-by-step explanation:

what is (-5q-8) - (q+3)

Answers

The answer would be −6q−11

Answer:

-6q-11

Step-by-step explanation:

A certain psychological test measures empathy and

emotional intelligence. The score, S, of a randomly

selected senior student at a large university has a mean

of 123 and a standard deviation of 29. The score, F, of a

randomly selected first-year student at a large university

has a mean of 104 and a standard deviation of 34.

Suppose we randomly select one senior student and one

first-year student. We can consider Sand F to be

independent random variables.

Answers

As per the given standard deviation, the probability that the first-year student shows a higher emotional intelligence test score in a randomly selected senior/first-year pair is 0.72

Here we have given that the score, S, of a randomly selected senior student at a large university has a mean of 123 and a standard deviation of 29.

And the score, F, of a randomly selected first-year student at a large university has a mean of 104 and a standard deviation of 34.

Then the probability is calculated as,

=> 123/104

=> 1.182

Where as the based on the standard deviation, the value is calculated as

=> 29/34

=> 0.852

Then the total probability of the given situation is calculated as,

=> 0.852/1.182

=> 0.72

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5. Refer to the figure below. (show work)
Given: UVWX is a parallelogram, m A. Find m B. Find UV.
C. Find m D. Find YW.

Answers

Answer:

see explanation

Step-by-step explanation:

A

∠ UVX and ∠ WXV are alternate angles and are congruent , then

∠ UVX = ∠ WXV = 15°

∠ WVU = ∠ WVX + ∠ UVX = 24° + 15° = 39°

B

opposite sides of a parallelogram are congruent , then

UV = XW = 36

C

consecutive angles are supplementary , sum to 180° , then

∠ XUV + ∠ WVU = 180° , so

∠ XUV + 39° = 180° ( subtract 39° from both sides )

∠ XUV = 141°

D

diagonals bisect each other , so

YW = UY = 10

Which milk product will have approximately 15.36 grams of milk fat in an 80-gram serving?(Heavy Cream: 36.7%, Light Cream 19.2%, Whole Milk 3.5%, Low-Fat Milk 1.5%, Skim Milk 0.05%)

Answers

The Light cream with 19.2% content will have 15.36g of milk.

What are percentages?

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”

Given here Light cream as 19.2% of 80g

∴ 0.192×80=15.36g

Hence, The Light cream with 19.2% content will have 15.36g of milk.

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WZ and XR are diameters of circle C. The diagram is not drawn to scale.

Circle C is shown.
Radii are drawn from point C to point R at the right, point Z at the upper right, point Y at the upper left, point X at the left, and point W at the lower left.
Angle Y C Z measures 112 degrees.
Angle X C W measures 63 degrees.
Points X, C, and R are all on the horizontal diameter of the circle.


What is the measure of convex arc upper Z upper W upper X?
A. 355º
B. 5º
C. 292º
D. 243º

Answers

The measure of convex arc upper Z is 243⁰ Option D

How to find the measure of the angle?

We should be aware that a convex angle is the angles that are irregular in nature

Assume that  the radius of the given circle is r.

The central angle of the lower arc ZWX = 41+180 = 221⁰

Note that then central angle of the upper arc ZWX = 360- 221⁰

This implies that the central angle of the upper arc ZWX = 360-221 = 139⁰

Recall that Lenght of arc = A/360 *2*π*r

Where A is the angle made by the radii, r= radius of the circle

Arc length of upper ZWX:

Arc length of upper ZWX = 139π/180*r

Arc length of upper ZWX = 139πr/180

The lenght is (139*22)/ 180*7

= 3058/2360

= 245⁰

In conclusion the measure of the convex upper is 245⁰

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The scores on the last math quiz are summarized in the following frequency table:
Score
10 9
8
7
6
4 3 2 1 0
7
5
3 2
1
0
0
10
0
Frequency 6
The information is then put into the following histogram:
Frequency
5
4
3
210
1 2 3 4 5 6 7 8 9 10
5
1
Score

Answers

Therefore , the answer to the above problem is 5.75 for the mean and 9 for the median.

What is mean?

Regardless of whether many elements are discrete or continuous, averages can only be calculated for numeric variables. You may find this by dividing the amount of values present in the dataset by its total number of values in the data. It is possible to perform computations using either raw data or data that has been compiled into frequency tables. The average value in mathematics is obtained by adding up all the integers in a data set and dividing the total by the total number of numbers. For example, in the data below

Here,

Spread it all out here first:

4, 5, 6, 7, 7, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10

The mean is calculated by dividing total total by the total number of scores. Add up each number.

There are 16 numbers total, and they add up to 92. 92 / 16 = 5.75

To get the median, identify the middle number among all the other numbers.

Sadly, there is no "center number" given that there are 16.

Add the ninth and eighth numbers together, then divide by to find the middle.

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Mia brought n shirts that were originally priced at $26.99 each shirt was on sale for $5.99 off the original price that she bought them which expression can be used to find the total sale price of n shirts

Answers

The total sale price of n shirts can be found using the following expression:

total sale price = n * (26.99 - 5.99)

This expression first calculates the sale price of a single shirt by subtracting the discount from the original price, and then multiplies that value by the number of shirts to get the total sale price.

For example, if Mia bought 3 shirts, the total sale price would be 3 * (26.99 - 5.99) = 3 * 21 = 63.

Santiago has 5 11/16 cups of dough to make dumpling. If he uses 13/16 cups of dough for each dumplings how many dumplings can santiago make?

Answers

Santiago can make 7 dumplings

To find out how many dumplings Santiago can make, we need to divide the total amount of dough (5 11/16 cups) by the amount of dough used per dumpling (13/16 cups).

To do this, we can first convert the fractions to have a common denominator. In this case, the denominator of 13/16 is 16, so we can convert 5 11/16 to have a denominator of 16 as well:

5 11/16 = (5 * 16) + 11/16 = 80 + 11/16

Now we can divide:

(80 + 11/16) ÷ (13/16) = (80 + 11) ÷ 13 = 91 ÷ 13

So Santiago can make 91/13 dumplings. This can be simplified further to 7 dumplings. So Santiago can make 7 dumplings with 5 11/16 cups of dough.

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The probability that a carton of eggs taken from the cooler at a store will have at least one cracked egg is 2.5%.
What are the odds that a carton of eggs will have at least one cracked egg?

Answers

Answer: The odds of an event happening are the ratio of the number of ways the event can happen to the number of ways it cannot happen.

Odds = (probability of success) / (probability of failure)

In this case, the event is that a carton of eggs will have at least one cracked egg.

The probability of success (the event happening) is 2.5%

The probability of failure (the event not happening) is 100% - 2.5% = 97.5%

so we can find the odds by dividing the probability of success by the probability of failure.

Odds = 2.5 / 97.5 = 0.025/0.975 = 1/39

So the odds that a carton of eggs will have at least one cracked egg is 1:39, meaning that for every 39 cartons that are free of cracked eggs, one carton will have at least one cracked egg.

It means that it's 1 in 39 chance that a carton of eggs will have at least one cracked egg

Step-by-step explanation:

Naomi'sbillforlunchatarestaurantwas$46.Sheleftan18%tip.Whatwastheamountofthetip?

Answers

Answer:

$8.28

Step-by-step explanation:

0.18*46=8.28

A white cylindrical silo has a diameter of 30 feet and a height of 80 feet. A red stripe with a horizontal width of 3 feet is painted on the silo, as shown, making two complete revolutions around it. What is the area of the stripe in square feet
The provided solution says that
The cylinder can be "unwrapped" into a rectangle, to get a stripe that is a parallelogram with base 3 and height 80.
However, I don't understand how the height of the stripe can be eighty. The distance from the top of the cylinder to the bottom is 80 feet as given, so how can a winded stripe that goes around be also 80 feet? Isn't the shortest distance, 80 ft, simply from the top to the bottom? How does a winded spiral also become 80 feet ?

Answers

The stripe's area in square feet is 240 square units.

What is area?

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina. The total space occupied by a flat (2-D) surface or the form of an item is defined as its area. Draw a square on a sheet of paper using a pencil. It is a two-dimensional figure. The area of the form on the paper is referred to as its Area. Consider your square to be made up of smaller unit squares.

Here,

The cylinder can be "unwrapped" into a rectangle, and we see that the stripe is a parallelogram with base 3 and height 80.

area=3*80

=240 square units.

the area of the stripe in square feet is 240 square units.

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Is Y =- 2 vertical or horizontal?

Answers

y = − 2 is a horizontal line that crosses the -axis at -2.

Now, According to the question:

Let's know:

What is Horizontal lines?

If we are given the equation of y equal to a number, our graph will be a horizontal line. Is this equation a function? The answer would be yes since it passes the vertical line test. The vertical line test tells us if we draw a vertical line through any point of the graph and it goes through only one point at each line, then it is a function. If it passes through more than one point, it does not. The slope of a horizontal line is zero.

The given equation is Y = -2

y = 2 is a horizontal line that crosses the -axis at 2.

=>  y = − 2 is a horizontal line that crosses the -axis at -2.

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HELP 50 points :D
1. You have $25 to spend on snacks for movie night with 4 of your friends. If individual boxes of raisins are $1.50, find the amount of money that remains per person for popcorn and a drink.


2. The cost for a town’s soccer league banquet is $960. There are 60 players in the soccer league. Determine the cost per player for the town if each player pays $5 to attend the banquet.


3. To solve the equation 2/3(x−4)=−10, Izzy wants to multiply both sides of the equation by the reciprocal of the fraction. Name the reciprocal.

__/__


4. There are 2 types of tickets to attend an awards dinner—silver and gold. The gold tickets are $8 more than the silver. If Patrick bought 10 tickets at each level and spent a total of $140, find the price of each ticket.(1 point)

$___ for each silver ticket and $___ for each gold ticket


5. Kendra is making bread, but the recipe she’s using makes 4 loaves. She only wants to make one loaf. The changed recipe calls for 2 1/2 cups of flour and sugar combined. If the original recipe calls for 2 cups of sugar, find the amount of flour (in cups) in the original recipe.

Answers

1. You have $25 to spend on snacks for movie night with 4 of your friends. If individual boxes of raisins are $1.50, find the amount of money that remains per person for popcorn and a drink.

To find the amount of money that remains per person after buying raisins, we first need to find the total cost of the raisins. If 4 boxes of raisins cost $1.50 each, then 4*1.50 = $6 is spent on raisins.

To find the amount of money that remains for popcorn and drinks, we subtract the cost of the raisins from the total amount of money: 25-6 = $19.

Since there are 5 people in total (you and 4 friends), we divide the remaining money by 5 to find the amount per person: 19/5 = $3.80 per person.

How calculate the cost?

2. The cost for a town’s soccer league banquet is $960. There are 60 players in the soccer league. Determine the cost per player for the town if each player pays $5 to attend the banquet.

To find the cost per player, we divide the total cost of the banquet by the number of players: 960/60 = $16 per player

3. To solve the equation 2/3(x−4)=−10, Izzy wants to multiply both sides of the equation by the reciprocal of the fraction. Name the reciprocal.

The reciprocal of the fraction 2/3 is 3/2

4. There are 2 types of tickets to attend an awards dinner—silver and gold. The gold tickets are $8 more than the silver. If Patrick bought 10 tickets at each level and spent a total of $140, find the price of each ticket.

Let's call the cost of a silver ticket x.

The cost of a gold ticket is x + 8.

We know that Patrick spent 10x + 10(x+8) = $140

We can simplify that: 10x + 10x + 80 = 140

Then we have 20x + 80 = 140

Then we have 20x = 60

And x = 3

Then the price of a silver ticket is $3 and the price of a gold ticket is $3+8 = $11

5. Kendra is making bread, but the recipe she’s using makes 4 loaves. She only wants to make one loaf. The changed recipe calls for 2 1/2 cups of flour and sugar combined. If the original recipe calls for 2 cups of sugar, find the amount of flour (in cups) in the original recipe.

If the original recipe calls for 2 cups of sugar and the changed recipe calls for 2 1/2 cups of flour and sugar combined, then the original recipe calls for 2 1/2 - 2 = 1/2 cup of flour.

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need help with these three

Answers

19) Multiplication is the same as division just the other way around. When I say this I literally mean it like we could use 45 x 2 which equals 90. Now if we look at it from division we would have to divide the answer we got with the smaller number of the multiplication. That would be 2 in this case. So it would be 90 divided by 2 equals 45. Hope I helped!

Is the Z or Y axis vertical?

Answers

Answer:

yes!

Step-by-step explanation:

the y axis vertical, and the x axis is horizontal!

A piggy bank contains 22 dimes, 7 nickels and 15 quarters. This morning you removed 8 dimes and 3 nickels. Which expression correctly shows the amount remaining in the piggy bank?

Answers

The expression that correctly shows the amount remaining in the piggy bank will be; 22d + 7n + 15q - (8d + 3n) = $4.85

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given that piggy bank contains 22 dimes, 7 nickels and 15 quarters. This morning you removed 8 dimes and 3 nickels.

LEt consider

dimes = d

→ nickels = n

quarters = q

Now the expression will be;

22 dimes + 7 nickels + 15 quarters - 8 dimes - 3 nickels

22d + 7n + 15q - 8d - 3n = $4.85

22d + 7n + 15q - (8d + 3n) = $4.85

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To get an A in her math class, Jada needs to have at least 90% of the total number of points possible. The table shows Jada’s results before the final test in the class.

1. ) Does Jada have 90% of the total possible points before the final test? Explain how you know.

2. ) Jada thinks that if she gets at least 92 out of 100 on the final test, she will get an A in the class. Do you agree? Explain

Answers

1) Jada does not have 90% of the total possible points before the final test.

2) If Jada gets at least 92 out of 100 on the final test, she will not get an A in the class.

From the following table of Jada’s results before the final test in the class the total number of points possible:

150 + 100 + 100 + 100 = 450

And Jada’s total points before the final test:

141 + 87 + 81 + 91 = 400

To check whether Jada have 90% of the total possible points before the final test, we find the percentgae of  Jada’s total points.

(400/450) × 100 = 88.89%

This means, Jada does not have 90% of the total possible points before the final test.

After final test, the total number of points possible:  450 + 100 = 550

And if she gets at least 92 out of 100 on the final test, her total points would be,

400 + 92 = 492    

And the percentgae of  Jada’s total points would be,

(492/550) × 100 = 89.45%

Given that Jada needs to have at least 90% of the total number of points possible.

so, she will notl get an A in the class.

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The diameter of the cylinder barrel was 20 in. When the barrel was lifted away it left an imprint of a circle on the ground. What is the area of the circle?

Answers

The area of the circle is  1256.64 square inches.

What is a Circle ?

All points on a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

A closed 2D form that isn't a polygon is a circle. It has one face that curves.If two circles have the same radius, they are said to be congruent.Equal chords are always located equally from the circle's center.The center of the circle is the perpendicular bisector of a chord.The line joining the points of two overlapping circles will be perpendicular to the line joining the points of the circles' centers.The tangents drawn at the diameter's endpoints are perpendicular to one another.

One of the most fundamental curvilinear geometric forms, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its basis in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.

The diameter of the cylindrical barrel is 20 in

So the diameter of the circular base is 20 in = 10 inches in radius.

Area of the circle = [tex]\pi\ r^{2}[/tex] =  π*20*20 = 1256.64 square inches.

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Graph the solution to this inequality on the number line.
-4x> 8.4
-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3

Answers

The Graph solution to this inequality on the number line is lies between -4 > 8.4 and their numbers are -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3.

How do you graph an inequality's solution on a number line?

Draw a circle around the number to indicate an inequality, such as x>3, on a number line (e.g., 3). In case the sign also states equal to, complete the circle (or ). If the sign doesn't include equal to (> or), leave the circle empty.

How would one graph an inequality?

When plotting an inequality, use the,, >, or sign as a = sign. If the inequality is either or, graph the equation as a dotted line. If the inequality is either or, graph the equation as a solid line.

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Does 4 8 12 make triangles?

Answers

No, a triangle with side length 4 units, 8 units , and 12 units does not exist.

As given in the question,

Let us consider the triangle be ABC,

Side length of the triangle are given as follow:

AB = 4units

BC = 8units

CA = 12units

Triangle inequality for the given triangle ABC is given by:

AB + BC > CA

AB + CA > BC

CA + BC > AB

To check whether the given side length forms a triangle apply triangle inequality we get,

AB + BC

= ( 4 + 8 )units

= 12 units

= CA

Here triangle fails.

Therefore, the given side length does not forms a triangle.

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Question 3 A student solved a quadratic equation as shown here

Answers

Answer:

Didn't move the 12 on the other side of the equal sign to make

2x^2 + 5x - 12 = 0

the other steps error city.

Step-by-step explanation:

2x^2 + 5x - 12 = 0

(2x - 3)(x + 4)= 0

2x - 3 = 0

2x = 3

x = 3/2

x + 4 = 0

x = -4

Why do we use similarity transformation?

Answers

The goal of using similarity transformations is to make the evaluation of a matrix's eigenvalues less complicated. In fact, the computation of the eigenvalues would be instantaneous if a given matrix could be translated into a similar matrix in diagonal or triangular form.

A geometric similarity or a matrix transformation that produces a likeness are both covered by the term "similarity transformation."

A conformal mapping with a similarity transformation is one whose transformation matrix A' has the formula A'=BAB⁻¹, where A and A' are referred to as similar matrices.

Space-based items are converted to equivalent objects by similarity transformations. Fractals and iterated function systems have a lot to do with similarity transformations and the idea of self-similarity.

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can someone please help me ( check the link for the question

Answers

The equation of the line that passes through the point (3, 2) and is perpendicular to 3x + 5y = 15 is y = (5/3)x - 3

What is an equation of a line?

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The equation of the line is y = m(1)x + c

The line passes through (3, 2) and is perpendicular to 3x + 5y = 15.

This means,

3x + 5y = 15

5y = -3x + 15

y = (-3/5)x + 3

m(2) = (-3/5)

Now,

m(1) x m(2) = -1

m(1) = -1 / ((-3/5)

m(1) = 5/3

Now,

(3, 2) = (x, y)

y = m(1)x + c

2 = (5/3) x 3 + c

2 = 5 + c
c = 2 - 5

c = -3

Thus,

The equation of the line is y = (5/3)x - 3.

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Water leaking onto a floor forms a circular pool. The circumference of the pool increases at a rate 24 cm/min. How fast is the area of the pool increasing when the radius is 5 cm

Answers

The area of the pool increasing at the rate of 753.98 cm²/min when the radius is 5 cm

How quickly does the pool's area grow when the radius is 5 cm?

Given:

radius of the pool increases at a rate of 24 cm/min

To Find:

How quickly does the pool's area grow when the radius is 5 cm?

Solution:

we are given with the circular pool

hence the area of the circular pool =

A = πr²-----------------------------(1)

The area of the pool os increasing at the rate of 24 cm/min, meaning that the area of the pool is changing with respect to time t

so differentiating eq (1)  with respect to t , we have

dA/dt =π 2r dr/dt

we have to find  dA/dt    with  dr/dt  = 24 cm/min and  r =  5cm

substituting the values

dA/dt = π 2(5)24

dA/dt =  π 26*8

dA/dt =  π 240

dA/dt =240π

dA/dt = 753.98

The area of the pool increasing at the rate of 753.98 cm²/min when the radius is 5 cm

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